A particle moves in a circle of radius 4.0 cm clockwise at constant speed of `2 ms^(-1)`. If `hat(x)` and `hat(y)` are unit acceleration vectors along X-axis and Y-axis respectively (in `cms^(-2)`), find the acceleration of the particle at the instant half way between P and Q. Refer to Fig.5.14 (a).

Options

A. `-4 (hatx + haty)`
B. `4 (hatx + haty)`
C. `-(hatx + haty) (1)/(sqrt2)`
D. `(hatx + haty) 4`

Answer

C

Explanation

Acceleration vector `veca = (v^(2))/(R) (-hatR)`
`= - ((R "cos" 45 hatx + R "sin" 45 haty))/(R) = -(hatx + haty) (1)/(sqrt2)`